At present, most social network games are, in essence, light sim/tycoon style games. You control a map on which you may build structures, place decorations, plant crops, and so on; some of the items you place produce game money, which you accumulate by clicking on the item in question after some period of time.
Sometimes, but not always, you have an avatar, who moves around, performing the "work" you request when you click on an item. You level up over time, and this gives you access to more placeable items and other content. Typically, there are badges, collectibles, and quests you may accomplish.
In other words, the core gameplay is inherently solitaire in nature; you do not cooperate with others in building your business/city/what have you, but are doing so on your own, each player in his own atomistic world.
However, social tycoon games provide many hooks for inter-player interaction, of a kind. One critical system is "gifting"; players are urged to send others free gifts, which cost the recipient nothing but provide some modest game benefit to the recipient.
In particular, the construction of critical items in a game are often gated by the requirement to have some number of a particular item that can only be received as a gift, giving players a motivation to request such gifts -- and, of course, to spend real money to eliminate the restriction if they have a small number of friends or are simply impatient.
Players may, of course, brag about their accomplishments, which serves the purpose of spamming social network communication channels with posts about the game, thereby helping to attract new players (a practice still encouraged by social tycoon games, despite the fact that Facebook now makes these posts invisible to non-players, thereby nerfing their viral function).
And players may "visit" each other's maps, performing some limited number of tasks on each friend's map. This provides some sense that other players exist in the same game world, although in truth each map is wholly independent and solitary.
If you look at the interplayer communication fostered by social tycoon games, you will see that every possible communication, every game action that a player may take relative to another player, exists solely to serve the purposes of the developers. Each communication action is designed to do one of three things: attract new players (virality), encourage players to return (retention), or encourage purchase (monetization).
Player interaction has modest, if any, impact on game progress; no impact on game outcomes; no or virtually no consequences for the players involved.
If SNRPGs are, truthfully, antisocial, social tycoon games are, truthfully, asocial; the interplayer interactions they foster are not, in fact, social in nature, do nothing to build friendships or enmity, and provide scant, if any, sense of connection to other people. They're like soloing in an MMO; you're aware of the presence of others, but they are largely irrelevant to your play.
Developers of social games have clearly given great thought to using the social graph to foster player acquisition, retention, and monetization; but as far as I can see, no thought whatsoever has given to the use of player connections to foster interesting gameplay. It's all about the money, and not at all about the socialization.
The peculiarity of this is that social networks are actually far better suited than most online environments to fostering social gameplay. Messaging and chat are built into the system, and need not be separately implemented by developers; but more importantly, the social graph allows players to interact with people who are their actual friends.
Most other online environments make that difficult. For example, MMOs make it hard to play with true friends, because of their segmented nature. I may learn that you are a WoW player, and want to play with you, but find that you play on a different server from me; I'd have to start over at level 1 to play with you.
Even if I and a group of friends all decide to start out on the same server, the reality is that we play on different schedules and with different levels of intensity, so even all starting at level 1, we will soon be of divergent power, and MMOs gate content by level. If you are level 5 and I am level 20, there's no easy way for us to play together, since progress for my character requires me to be in areas of the world that will kill your character quickly.
On a social network, it is easy to discover what games your friends play, and it would be trivial to implement systems to allow people to play with each other -- reserving games for groups of friends, say, or designing systems to accommodate players of diverse power who are network friends.
Online sites that allow quick, pick-up and play games are problematic as well; it's easy to go to a site like Pogo.com or Days of Wonder and play with strangers, but this is far less interesting and enjoyable than playing with friends. The messaging provided by social networks, and the ability to share content with others, means it should be far easier to implement games that allow play with genuine friends than on other sites.
In short, developers have learned how to use the social graph to rake in the bucks, but not how to use it to foster gameplay that is actually social.